I have tried to solve this equation $ 2^n-1=0\bmod (n^2-1) $ , I got using wolfram alpha $n=2,4,16,36$ seems the solution are $0 \bmod 4$ however 8 is not a solution, probably there are only finitely many solutions. Now, how do I get other solutions if it has finitely many solutions?
2026-04-03 21:23:15.1775251395
When is $ 2^n-1=0\bmod (n^2-1) $?
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The sequence of numbers that solve your equation is OEIS A247219. A note there says
So there are infinitely many solutions.